// URL: https://yukicoder.me/problems/no/665 import std.algorithm, std.array, std.bitmanip, std.container, std.conv, std.format, std.functional, std.math, std.range, std.traits, std.typecons, std.stdio, std.string; version(unittest) {} else void main() { long n; int k; io.getV(n, k); auto fact = Fact!mint(k+2); auto b = new mint[](k+1); b[0] = 1; foreach (i; 1..k+1) { if (i >= 3 && i%2 == 1) continue; foreach (j; 0..i) if (i == 1 || i%2 == 0) b[i] -= fact.combi(i+1, j)*b[j]; b[i] *= mint(i+1).inv; } auto s = mint(0), nb = mint(n+1); foreach_reverse (i; 0..k+1) { if (i == 1 || i%2 == 0) s += fact.combi(k+1, i)*b[i]*nb; nb *= mint(n+1); } s *= mint(k+1).inv; io.put(s); } struct Fact(T, bool inv = true) { int n; T[] table; alias table this; static if (inv) T[] invTable; pure nothrow @safe { this(int n) { this.n = n; table = new T[](n+1); table[0] = 1; foreach (i; 1..n+1) table[i] = table[i-1]*i; static if (inv) { invTable = new T[](n+1); invTable[n] = T(1)/table[n]; foreach_reverse (i; 1..n+1) invTable[i-1] = invTable[i]*i; } } } pure nothrow @nogc @safe { static if (inv) { T perm(size_t a, size_t b) in { assert(n >= a && a >= b); } do { return table[a]*invTable[a-b]; } T combi(size_t a, size_t b) in { assert(n >= a && a >= b); } do { return table[a]*invTable[b]*invTable[a-b]; } T homo(size_t a, size_t b) in { assert(n >= a+b-1); } do { return combi(a+b-1, b); } } } } const mod = 10^^9+7; alias mint = ModInt!mod; pure nothrow @nogc @safe { auto lowerBoundBy(alias conv = "a", alias comp = "a tuple(e, convFun(e))).assumeSorted!((a, b) => compFun(a[1], b[1])); } } pure nothrow @nogc @safe { T isqrt(T)(T n) if (is(T == int) || is(T == long)) { static if (is(T == int)) auto max = 46_341; else static if (is(T == long)) auto max = 3_037_000_500L; return iota(T(0), max).lowerBoundBy!("a^^2", "a<=b")(n).back; } T icbrt(T)(T n) if (is(T == int) || is(T == long)) { static if (is(T == int)) auto max = 1_291; else static if (is(T == long)) auto max = 2_097_152L; return iota(T(0), max).lowerBoundBy!("a^^3", "a<=b")(n).back; } ExtGcdResult!T extGcd(T)(T a, T b) { if (a == 0) { return ExtGcdResult!T(b, T(0), T(1)); } else { auto r = extGcd(b%a, a); return ExtGcdResult!T(r.gcd, r.y-(b/a)*r.x, r.x); } } struct ExtGcdResult(T) { T gcd, x, y; } } pure nothrow @safe { T powr(alias pred = "a*b", T, U)(T a, U n, T one) { alias predFun = binaryFun!pred; if (n == 0) return one; auto r = one; for (; n > 0; n >>= 1) { if (n&1) r = predFun(r, a); a = predFun(a, a); } return r; } T powr(alias pred = "a*b", T, U)(T a, U n) { return powr!(pred, T, U)(a, n, T(1)); } } struct ModInt(int m, bool pos = false) { pure nothrow @nogc @safe: @property int value() { return i; } @property void value(int v) { i = nm(v); } alias value this; this(T)(T v) if (isIntegral!T) { i = nm(v); } ref Mint opAssign(T)(T v) if (isIntegral!T) { i = nm(v); return this; } ref Mint opAssign(Mint v) { i = v.i; return this; } static if (!pos) { Mint opUnary(string op: "-")() const { return Mint(-i); } } static if (m < int.max / 2) { Mint opBinary(string op, T)(T r) const if ((op == "+" || (!pos && op == "-")) && isIntegral!T) { return Mint(mixin("i"~op~"r")); } ref Mint opOpAssign(string op, T)(T r) if ((op == "+" || (!pos && op == "-")) && isIntegral!T) { i = nm(mixin("i"~op~"r")); return this; } } else { Mint opBinary(string op, T)(T r) const if ((op == "+" || (!pos && op == "-")) && isIntegral!T) { return Mint(mixin("l"~op~"r")); } ref Mint opOpAssign(string op, T)(T r) if ((op == "+" || (!pos && op == "-")) && isIntegral!T) { i = nm(mixin("l"~op~"r")); return this; } } Mint opBinary(string op: "*", T)(T r) const if (isIntegral!T) { return Mint(l*r); } ref Mint opOpAssign(string op: "*", T)(T r) if (isIntegral!T) { i = nm(l*r); return this; } Mint opBinary(string op)(Mint r) const if (op == "+" || !pos && op == "-" || op == "*") { return opBinary!op(r.i); } ref Mint opOpAssign(string op)(Mint r) if (op == "+"|| !pos && op == "-" || op == "*") { return opOpAssign!op(r.i); } Mint opBinary(string op: "^^", T)(T n) if (isIntegral!T) { return powr(this, n, Mint(1)); } static if (!pos) { Mint opBinary(string op: "/")(Mint r) { return Mint(l*r.inv.i); } ref Mint opOpAssign(string op: "/")(Mint r) { i = nm(l*r.inv.i); return this; } Mint opBinary(string op: "/", T)(T r) if (isIntegral!T) { return opBinary!op(Mint(r)); } Mint opOpAssign(string op: "/", T)(T r) if (isIntegral!T) { return opOpAssign!op(Mint(r)); } Mint inv() { return Mint(extGcd(i, m).x); } } private { alias Mint = ModInt!(m, pos); version(BigEndian) union { long l; struct { int i2; int i; } } else union { long l; int i; } pure nothrow @nogc @safe { int nm(T)(T v) const if (isIntegral!T) { static if (pos) return cast(int)(v%m); else return cast(int)((v%m+m)%m); } } } } auto io = IO!()(); import std.stdio; struct IO(alias IN = stdin, alias OUT = stdout) { import std.meta : allSatisfy; import core.stdc.stdlib : exit; void getV(T...)(ref T v) { foreach (ref w; v) get(w); } void getA(T)(size_t n, ref T v) if (hasAssignableElements!T) { v = new T(n); foreach (ref w; v) get(w); } void getC(T...)(size_t n, ref T v) if (allSatisfy!(hasAssignableElements, T)) { foreach (ref w; v) w = new typeof(w)(n); foreach (i; 0..n) foreach (ref w; v) get(w[i]); } void getM(T)(size_t r, size_t c, ref T v) if (hasAssignableElements!T && hasAssignableElements!(ElementType!T)) { v = new T(r); foreach (ref w; v) getA(c, w); } template getS(E...) { void getS(T)(size_t n, ref T v) { v = new T(n); foreach (ref w; v) foreach (e; E) mixin("get(w."~e~");"); } } const struct PutConf { bool newline = true, flush, exit; string floatFormat = "%.10f", delimiter = " "; } void put(alias conf = "{}", T...)(T v) { mixin("const PutConf c = "~conf~"; putMain!c(v);"); } void putB(alias conf = "{}", S, T)(bool c, S t, T f) { if (c) put!conf(t); else put!conf(f); } void putRaw(T...)(T v) { OUT.write(v); OUT.writeln; } private { dchar[] buf; auto sp = (new dchar[](0)).splitter; void nextLine() { IN.readln(buf); sp = buf.splitter; } void get(T)(ref T v) { if (sp.empty) nextLine(); v = sp.front.to!T; sp.popFront(); } void putMain(PutConf c, T...)(T v) { foreach (i, w; v) { putOne!c(w); if (i+1 < v.length) OUT.write(c.delimiter); } static if (c.newline) OUT.writeln; static if (c.flush) OUT.flush(); static if (c.exit) exit(0); } void putOne(PutConf c, T)(T v) { static if (isInputRange!T && !isSomeString!T) putRange!c(v); else static if (isFloatingPoint!T) OUT.write(format(c.floatFormat, v)); else static if (hasMember!(T, "fprint")) v.fprint(OUT); else OUT.write(v); } void putRange(PutConf c, T)(T v) { auto w = v; while (!w.empty) { putOne!c(w.front); w.popFront(); if (!w.empty) OUT.write(c.delimiter); } } } }